That looks like a lot of weeds and very little grass for 3-4 weeks of progress. I think you need to get rid of the weeds now, then reseed the grass, top the seeds with a hay mulch, and water according to the seed recommendations. The hay mulch will help keep the seeds’ moisture consistent, and will help keep down the weeds while the grass gets started.

What's your locale? If a southern lawn, you're kind of late for seeding. If a northern lawn, very early. :-)

What type of grass did you use, and how much sun does the area get?

I do note you said for a low-moisture area. New seed really needs to be kept damp during germination and should be watered, if in a dry area, up to 3 times per day during that germination period. Depending on the seed types, that can range from 7 to 28 days.

I wouldn't recommend hay mulch. If you want to see weeds, use hay mulch. Even the weed free stuff has been awful for me. Peat moss is great, though. Compost as well, although occasional weeds are an issue with it. And if you want to use the grass soil as a topdressing, that's also completely workable. It's a nice, moisture-retaining soil.

thanks all for your replies. we are located in southern new jersey. what is the suggested method of getting rid of the weeds? a contributor to a former post suggested that scott's topsoil is not soil but rather composted wood products. this is what we used prior to seeding - in case this information changes anything. lastly, if all continues to fail, can sod be placed on top of this mess?

I guess it would be better if you get rid of the weeds now.

With grass that young, manual removal is your only option. Any chemical you use will damage the grass along with the weeds.

And it's fine to topdress with composted wood.

You can place sod atop that but, again, you're going to have to keep sod damp until it roots. The failure here seems to be a lack of water and sod will also fail if not watered.

Wait until late August before you do anything.

what if we re-seed, do a lot of watering, and then when the grass grows in deal with all the weeds then?

The best procedure is to water the area and wait for weeds. Then Roundup the area to kill the weeds. Water again for maybe a week and get more weeds to germinate. Roundup again. By this time you've gotten rid of most weeds. Then you seed and proceed as normal with watering. You can't do any of this in the summer when it is 90 - 100 degrees. The new grass will likely die from the heat. Just kill the area off a couple of times and then in late August, just a few weeks away, when nighttime temps start to cool off a little, go ahead and seed the area.

This all presumes you are trying to grow grass somewhere with some sun, and not right up against a house with northern exposure.